Question

A sum of Rs 1,200 was lent partly at 5% and partly 6% simple interest. The total interest received after 2 years was Rs 128. The ratio of the money lent out at 5% and 6% is

• A. 5:6
• B. 6:5
• C. 2:1
• D. 1:2

Answer 1

Answer: (C)

2:1

Let the second part be $Rs.x$. Then first part is $Rs.(1200-x)$

So interest on first part $=\frac{(1200-x)\times 5\times 2}{100}=\frac{(1200-x)}{10}$

And interest on second part $=\frac{\left(x\right)\times 6\times 2}{100}=\frac{3\left(x\right)}{25}$

Now, according to question:

$\frac{(1200-x)}{10}+\frac{3x}{25}=128$

Taking $LCM$ and solving further, we get:

$\Rightarrow 5(1200-x)+6x=128\times 50$

$\Rightarrow 6000-5x+6x=6400$

$\Rightarrow x=400$.

So, second part is $Rs.400$.

Hence, first part is $(1200-x)=Rs.800$

Hence ratio of first part to second part is $800:400=2:1$